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Calculus and Optimization for Machine Learning
Week 2
Practice Quiz #1

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Practice Quiz #1

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Practice Quiz #1

Total points 3

1.

Question 1

Compute $\lim\limits_{x \to \infty} \sin \sqrt{x+1}-\sin \sqrt{x}$ (if the limit does no exist, write $-1000$ ).

1 / 1 point

0

0

Correct

Correct!

2.

Question 2

Compute $\lim\limits_{x\to \infty} \left( \frac{x-a}{x+a} \right)^{x}$ (if the limit does no exist, write $-1000$ ).

1 / 1 point

e^{- 2 a}

E^(-2*a)

Correct

Correct!

3.

Question 3

Compute $\lim\limits_{x\to\pi} \frac{\sin nx}{\sin mx}$ (your answer should not contain any functions, only signs, numbers and parameters, if the limit does no exist, write $-1000$ ).

1 / 1 point

\frac{n}{m} \left(-1\right)^{- m + n}

(-1)^(n-m)*(n/m)

Correct

Correct!